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Solutions for Session 3, Part E
See solutions for Problems: E1 | E2 | E3 | E4 | E5 | E6 | E7 | E8 | E9 | E10 | E11
E12 | E13 | E14 | E15 | E16
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Problem E1 | |
In each case there are clear reasons that there can only be one answer. For example, a state can have only one capital city. A word can only have one first letter.
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Integer | | Odd or Even |
1 | | odd |
2 | | even |
3 | | odd |
4 | | even |
5 | | odd |
10 | | even |
15 | | odd |
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SSN | | DOB |
590-14-6017 | | 6/2/75 |
024-33-3467 | | 10/27/70 |
024-33-3568 | | 10/27/70 |
024-33-7146 | | 8/10/74 |
036-89-0831 | | 6/8/84 |
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State | | Capital |
Massachusetts | | Boston |
Texas | | Austin |
Washington | | Olympia |
North Dakota | | Bismarck |
West Virginia | | Charleston |
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Side Length | | Area |
1 | | 1 |
2 | | 4 |
3 | | 9 |
4 | | 16 |
5 | | 25 |
10 | | 100 |
15 | | 225 |
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Word | | First Letter |
Word | | W |
Hey | | H |
Wow | | W |
Math | | M |
Is | | I |
Very | | V |
Cool | | C |
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<< back to Problem E1
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Problem E2 | |
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Sure, but not always. The odd-or-even, date of birth, and letter functions have the possibility of matching outputs.
<< back to Problem E2
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Problem E3 | |
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More tables!
For certain (not necessarily all!) inputs, there can be more than one correct output. Note how different this is from Algorithms A and B.
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Number | | Smaller Number |
10 | | 7 |
10 | | 8 |
15 | | 10 |
17 | | 12 |
21 | | 12 |
21 | | -5 |
0 | | -100 |
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Number | | Factor |
15 | | 3 |
20 | | 5 |
24 | | 3 |
24 | | 4 |
30 | | 10 |
45 | | 9 |
100 | | 20 |
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Person | | Grandparent |
Abbey | | Mary |
Abbey | | John |
Megan | | Mary |
Megan | | Alice |
Brian | | Henry |
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City Name | | State Name |
New York | | New York |
Chicago | | Illinois |
Salem | | Massachusetts |
Salem | | Oregon |
Portland | | Oregon |
Portland | | Maine |
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Side Length | | Area |
5 | | 20 |
10 | | 20 |
20 | | 20 |
1 | | 1/4 |
5 | | 15 |
10 | | 50 |
100 | | 250000 |
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Word | | Anagram |
ear | | are |
ear | | era |
mare | | ream |
toilets | | T. S. Eliot |
relation | | oriental |
listen | | silent |
Elvis | | lives |
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<< back to Problem E3
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Problem E4 | |
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Other functions: a circle's circumference is a function of its radius; the average temperature is a function of the time of year; a TV program's rating is a function of the number of people watching the show. For each function, there can only be one output for a given input, while a non-function may have more than one output for the same input. For example, people of more than one age can wear size 11 shoes.
<< back to Problem E4
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Problem E5 | |
a. | The output is yes, 3 is a prime number. |
b. | The output is yes, 2 is a prime number. |
c. | No, 100 is not a prime (it has lots of factors). |
d. | No, 1 is not a prime (it needs to have exactly two factors). |
<< back to Problem E5
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Problem E6 | |
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It could be any prime number: 2, 3, 5, 7, 11, 13, 17, 19, ... .
<< back to Problem E6
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Problem E7 | |
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It's a function because there is exactly one output. The answer is always "yes" or "no," never both.
<< back to Problem E7
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Problem E8 | |
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There is no such function. The outputs are only "yes" or "no," so if such a function existed, it would have to guarantee the specific prime number picked from "yes," which is impossible. Put another way, the undoing rule cannot be a function, because "yes" would return all the prime numbers, and "no" would return all the non-primes.
<< back to Problem E8
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Problem E9 | |
a. | The output is 3. |
b. | The output is 3. |
c. | The output is still 3. |
<< back to Problem E9
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Problem E10 | |
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It could be any number at all. Since the output is always 3, telling us that the output is 3 doesn't give any new information. This is the same situation as Problem D5.
<< back to Problem E10
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Problem E11 | |
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There is exactly one value for the output. It's always 3, but that doesn't keep it from being a function.
<< back to Problem E11
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Problem E13 | |
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The output is a triangle whose sides are 1/2 the sides of the original and parallel to the original sides.
<< back to Problem E13
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Problem E14 | |
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All the sides are half as long, and the new triangle's area is one-fourth of the original.
<< back to Problem E14
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Problem E16 | |
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Yes, because there is exactly one output polygon for any starting polygon.
<< back to Problem E16
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